A Commentary on the Passing Scene by
Robert Paul Wolff
rwolff@afroam.umass.edu

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The following books by Robert Paul Wolff are available on Amazon.com as e-books: KANT'S THEORY OF MENTAL ACTIVITY, THE AUTONOMY OF REASON, UNDERSTANDING MARX, UNDERSTANDING RAWLS, THE POVERTY OF LIBERALISM, A LIFE IN THE ACADEMY, MONEYBAGS MUST BE SO LUCKY, AN INTRODUCTION TO THE USE OF FORMAL METHODS IN POLITICAL PHILOSOPHY.Now Available: Volumes I, II, III, and IV of the Collected Published and Unpublished Papers.

NOW AVAILABLE ON YOUTUBE: LECTURES ON KANT'S CRITIQUE OF PURE REASON. To view the lectures, go to YouTube and search for "Robert Paul Wolff Kant." There they will be.

NOW AVAILABLE ON YOUTUBE: LECTURES ON THE THOUGHT OF KARL MARX. To view the lectures, go to YouTube and search for Robert Paul Wolff Marx."

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Tuesday, February 4, 2014

THE PRISONER'S DILEMMA PART TWO

To see how beguiled we can
be by irrelevant stories, consider the following outcome matrix, derived from a
variant of the story we have been dealing with:

B1

B2

A1

A serves one day and B
serves one day

A serves 40 years and a
day and B goes free

A2

A goes free and B serves
40 years and a day

A serves 40 years and B
serves 40 years

In this variant, if both criminals
keep their mouths shut, they go free after only one night in jail.If they both rat, they spend forty years in
jail.If one rats and the other doesn't,
the squealer goes free today and the other serves 40 years and a day.Both criminals know this, of course, because
the premise of the game is that this is Decision Under Uncertainty, meaning
that they know the content of the outcome matrix and of the payoff matrix but
not the choice made by the other player. The structure of the payoff matrix associated
with this outcome matrix is supposed to be identical with that associated with
the original story, namely:For A, O21
> O11 > O22 > O12, and for B, O12 >O11 >O22 > O21, because
the premise of the little example is that each player rates the outcomes solely
on the basis of the length of his or her sentence, regardless of how long or short that is.It is therefore still the case that O11 is
preferred by both players to O22, and it is still the case that IF each player's preference order is
determined solely by a consideration
of that player's sentencing possibilities [and that each player prefers less
time in jail to more], and that each player chooses a strategy solely by attending to considerations
of dominance, then the two of them will end up with a Pareto sub-optimal
result.But how likely is all of that to
occur in the real world?I suggest the
answer is, not likely at all.For the
upshot of the game to remain the same, we must assume two things, neither of
which is even remotely plausible in any but the most bizarre
circumstances:First, that each player
is perfectly prepared to condemn his or her partner in crime to a sentence of
40 years and a day just to have a chance at reducing a one day sentence to
zero;and second, that the two of them,
faced with this extraordinary outcome matrix, cannot coordinate on the Pareto
Preferred Outcome without the benefit of communication.

What would happen in the real
world?I suggest something like this
might happen:A examines the outcome
matrix and says to herself:"Look, there
is no difference to speak of between a 40 year sentence and a sentence of 40
years and a day. I am going to count on
my partner to be sensible, and go for the one day sentence.The very worst that can happen is that I will
have a day tacked onto the end of forty years, if I am still alive then, but I
have a good shot here at getting off all but scot free."

Now, from a Game Theoretic point of
view, this is not interesting at all.What is the point of introducing outcome matrices and payoff matrices
and dominant strategies and Pareto sub-optimal outcomes if, when it gets right
down to it, we are going to go into all the messy details of who the players
are, what their relation to one another is, what history they have with one
another, and all the rest of it?I
thought Game Theory was going to enable me to analyze the situation without any
of that stuff.

This is a point of such importance
that I need to talk about it for a bit.A very long time ago, Aristotle and Pythagoras and some other smart
Greeks [and also some really smart Egyptians, but I don't want to get into the
whole Black Athena thing] discovered
that in some situations, one can successfully abstract from the details of a
problem and still carry out a valid process of reasoning about it by attending
only to certain formal or structural features of the situation.One can, for example, carry out long, complex
chains of reasoning about shapes and sizes and spatial relationships without
any reference to the materials in which these shapes and sizes and relationships
are embedded.Now, this was not obvious
on the face of it, when they made this historic discovery.You could not get very far reasoning about
crops, after all, if you failed to take notice of which crop you were talking
about, nor could you say much of interest about metalworking in abstraction
from the particular metal in question.But
if you know that all human beings are mortals, and you know that all Athenians
are human beings, then you can draw
the conclusion that All Athenians are mortal, just by attending to the formal
syntactic structure of your two premises, namely that All A are B and All B are
C, from which it follows, regardless of the details of the story you are
telling, that All A are C.

Formal reasoning of this sort is
beguiling, both because it is extremely powerful and because it can be engaged
in by people who do not actually know much about the way the world works.There is also a lot of not very sublimated
erotic and aggressive energy expressed here.Not for nothing do mathematicians speak about ramming an argument
through.Oh well.That could lead us in rather hairy
directions.

Once all of this has gained wide
acceptance and has been brought to its present height of complexity and
sophistication, everyone wants to get in on the act.I mean, who wants to talk about the psychological
profiles of accused individuals enmeshed in the complexities of the criminal
justice system when you can slap a 2 x 2 matrix on the page and carry out
abstract calculations about dominant strategies?How cool is that?This is the reason why philosophers, who have
long since learned that logicians have the highest status in their profession,
put backwards E's on the page and talk about "for all x" rather than
"everyone."

About Me

As I observed in one of my books, in politics I am an anarchist, in religion I am an atheist, and in economics I am a Marxist. I am also, rather more importantly, a husband, a father, a grandfather, and a violist.